PRINCIPLES OF PHYSICAL OPTICS

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1 PRINCIPLES OF PHYSICAL OPTICS C. A. Bennett University of North Carolina At Asheville WILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

CONTENTS Preface 1 The Physics of Waves 1 1.1 Introduction 1 1.2 One-Dimensional Wave Equation 2 1.2.1 Transverse Traveling Waves On A String 3 1.3 General Solutions to the 1-D Wave Equation 5 1.

2 CONTENTS Preface 1 The Physics of Waves Introduction One-Dimensional Wave Equation Transverse Traveling Waves On A String General Solutions to the 1-D Wave Equation Harmonic Traveling Waves The Principle of Superposition Periodic Traveling Waves Linear Independence Complex Numbers and the Complex Representation Complex Algebra The Complex Representation of Harmonic Waves The Three-Dimensional Wave Equation Three-Dimensional Plane Waves Spherical Waves 20 2 Electromagnetic Waves and Photons Introduction Electromagnetism 26 ix

$5 The Electromagnetic Spectrum 48 Appendix: Maxwell's Equations in Differential Form 53 3 Reflection and Refraction 59 3.1 Introduction 59 3.2 Overview of Reflection and Refraction 60 3.2.1 Fermat' s Principle of Least Time 63 3.$

3 X CONTENTS 2.3 Electromagnetic Wave Equations Transverse Electromagnetic Waves Energy Flow and the Poynting Vector Irradiance Photons Single-Photon Interference The Electromagnetic Spectrum 48 Appendix: Maxwell's Equations in Differential Form 53 3 Reflection and Refraction Introduction Overview of Reflection and Refraction Fermat' s Principle of Least Time Maxwell's Equations at an Interface Boundary Conditions Electromagnetic Waves at an Interface The Fresnel Equations Incident Wave Polarized Normal to the Plane of Incidence Incident Wave Polarized Parallel to the Plane of Incidence Interpretation of the Fresnel Equations Normal Incidence Brewster's Angle Total Internal Reflection Plots of the Fresnel Equations vs. Incident Angle Phase Changes on Reflection Reflectivity and Transmissivity Plots of Reflectivity and Transmissivity vs. Incident Angle The Evanescent Wave * Dispersion Dispersion in Dielectric Media Dispersion in Conducting Media Scattering Atmospheric Scattering Optical Materials Geometric Optics Introduction Reflection and Refraction at Aspheric Surfaces Reflection and Refraction at a Spherical Surface Spherical Reflecting Surfaces Spherical Refracting Surfaces 128

$6 Aberrations 143 4.6.1 Chromatic Aberration 143 4.6.2 Spherical Aberration 146 4.6.3 Astigmatism and Coma 147 4.6.4 Field Curvature 147 4.6.5 Diffraction 148 4.7 Optical Instruments 148 4.7.1 The Camera 148 4.$

4 CONTENTS XI Sign Conventions and Ray Diagrams Lens Combinations Thin-Lenses in Close Combination * Principal Points and Effective Focal Lengths Aberrations Chromatic Aberration Spherical Aberration Astigmatism and Coma Field Curvature Diffraction Optical Instruments The Camera The Eye The Magnifying Glass The Compound Microscope The Telescope The Exit Pupil *Radiometry Extended Sources Radiometry of Blackbody Sources Rayleigh-Jeans Theory and the Ultraviolet Catastrophe Planck's Quantum Theory of Blackbody Radiation * Optical Fibers * Thick Lenses *Principal Points and Effective Focal Lengths of Thick Lenses ""Introduction to Matrix Methods in Paraxial Geometrical Optics The Translation Matrix The Refraction Matrix The Reflection Matrix The Ray Transfer Matrix Location of Cardinal Points for an Optical System 189 Appendix: Calculation of the Jeans Number 197 Superposition and Interference Introduction Superposition of Harmonic Waves Interference Between Two Monochromatic Electromagnetic Waves Linear Power Detection Interference Between Beams with the Same Frequency Thin-Film Interference Quasi-Monochromatic Sources Fringe Geometry 211

XII CONTENTS 5.3.6 Interference Between Beams with Different Frequencies 212 5.4 Fourier Analysis 218 5.4.1 Fourier Transforms 218 5.4.2 Position Space, k-space Domain 219 5.4.3 Frequency-Time Domain 223 5.

5 XII CONTENTS Interference Between Beams with Different Frequencies Fourier Analysis Fourier Transforms Position Space, k-space Domain Frequency-Time Domain Properties of Fourier Transforms Symmetry Properties Linearity Transform of a Transform Wavepackets Group and Phase Velocity Interferometry * Energy Conservation and Complementary Fringe Patterns Single-Photon Interference Multiple-Beam Interference The Scanning Fabry-Perot Interferometer Interference in Multilayer Films Antireflection Films High-Reflectance Films Coherence Temporal Coherence Spatial Coherence Michelson's Stellar Interferometer Irradiance Interferometry Telescope Arrays 266 Appendix: Fourier Series 269 Diffraction Introduction Huygens' Principle Babinet's Principle Fraunhofer Diffraction Single Slit Rectangular Aperture Circular Aperture Optical Resolution More on Stellar Interferometry Double Slit N Slits: The Diffraction Grating The Diffraction Grating Fraunhofer Diffraction as a Fourier Transform Apodization 311

$CONTENTS XIII 6.4 Fresnel Diffraction 313 6.4.1 Fresnel Zones 315 6.4.2 Holography 325 6.4.3 Numerical Analysis of Fresnel Diffraction with Circular Symmetry 327 6.4.4 Fresnel Diffraction from Apertures with Cartesian Symmetry 329 6.$

6 CONTENTS XIII 6.4 Fresnel Diffraction Fresnel Zones Holography Numerical Analysis of Fresnel Diffraction with Circular Symmetry Fresnel Diffraction from Apertures with Cartesian Symmetry Introduction to Quantum Electrodynamics Feynman's Interpretation Lasers Introduction Energy Levels in Atoms, Molecules, and Solids Atomic Energy Levels Molecular Energy Levels Solid-state Energy Bands Semiconductor Devices Stimulated Emission and Light Amplification Laser Systems Atomic Gas Lasers Molecular Gas Lasers Solid-State Lasers Other Laser Systems Longitudinal Cavity Modes Frequency Stability Introduction to Gaussian Beams Overview of Gaussian Beam Properties Derivation of Gaussian Beam Properties Approximate Solutions to the Wave Equation Paraxial Spherical Gaussian Beams Gaussian Beam Focusing Matrix Methods and the ABCD Law Laser Cavities Laser Cavity with Equal Mirror Curvatures Laser Cavity with Unequal Mirror Curvatures Stable Resonators Traveling Wave Resonators Unstable Resonators Transverse Cavity Modes Optical Imaging Introduction Abbe Theory of Image Formation 400

XIV CONTENTS 8.2.1 Phase Contrast Microscope 405 8.3 The Point Spread Function 407 8.3.1 Coherent vs. Incoherent Images 407 8.3.2 Speckle 412 8.4 Resolving Power of Optical Instruments 413 8.

7 XIV CONTENTS Phase Contrast Microscope The Point Spread Function Coherent vs. Incoherent Images Speckle Resolving Power of Optical Instruments Image Recording Photographic Film Digital Detector Arrays Contrast Transfer Function Spatial Filtering Adaptive Optics Polarization and Nonlinear Optics Introduction Linear Polarization Linear Polarizers Linear Polarizer Design Birefringence Circular and Elliptical Polarization Wave Plates and Circular Polarizers Jones Vectors and Matrices Birefringent Colors The Electro-optic Effect Pockels Cells Kerr Cells Optical Activity Faraday Rotation Acousto-optic Effect Nonlinear Optics Harmonic Generation Phase Conjugation Reflection by Degenerate Four-Wave Mixing Frequency Mixing 478 References 483 Index 485

Optics.

Optics. Optics www.optics.rochester.edu/classes/opt100/opt100page.html Course outline Light is a Ray (Geometrical Optics) 1. Nature of light 2. Production and measurement of light 3. Geometrical optics 4. Matrix